https://neckpinch.com/authors/julian-scheuer/New arXiv papers by Julian Scheuer, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2604.15993arxiv:2604.15993Fri, 17 Apr 2026 00:00:00 GMTShujing Pan, Julian Scheuer — This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle θ∈(0,fracπ2]. Such hypersurfaces are called θ-capillary hypersurfaces and for those we introduce a new notion of convexity, which we call θ-horocap-convexity. For such hypersurfaces, we prove the convergence of a curvature flow of Guan/Li type with capillary boundary. Remarkably, we prove this result for a class of curvature functions which include all quotients of symmetric polynomials and, as a consequence, we obtain the full set of quermassintegral inequalities in the θ-horocap-convex case. In the strictly horocap-convex setting, we employ the flow to prove the geometric inequalities, while for the horocap-convex case and the characterization of the equality case, we develop new arguments which are interesting in their own right.Other curvature flowsFree boundary & capillaryGeometric inequalities https://arxiv.org/abs/2304.02414arxiv:2304.02414Wed, 05 Apr 2023 00:00:00 GMTWilhelm Klingenberg, Ben Lambert, Julian Scheuer — Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to its rays. Its boundary is required to have constant intersection angle with the boundary of the cone. We prove that the corresponding parabolic boundary value problem for the graph admits a solution for all time which rescales to a self-similarly expanding solution.Mean curvature flow3-manifoldsFree boundary & capillaryPhysics https://arxiv.org/abs/2211.17040arxiv:2211.17040Wed, 30 Nov 2022 00:00:00 GMTEsther Cabezas-Rivas, Julian Scheuer — We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space.Mean curvature flowVolume-preserving & constrained flowsSphere theoremsLong-time existence & convergenceGeometric inequalitiesPhysics